Lie related by stupid on purpose (12)
I believe the answer is:
deliberately
'on purpose' is the definition.
(synonyms)
'lie related by stupid' is the wordplay.
'stupid' indicates anagramming the letters (in a stupid order).
'lie'+'related'+'by'='lierelatedby'
'lierelatedby' is an anagram of 'DELIBERATELY'.
(Other definitions for deliberately that I've seen before include "as intended" , "Consciously and intentionally" , "On purpose" .)